Spectral analysis of the full gravity tensor

Details Spectral analysis of the full gravity tensor Spectral analysis of the full gravity tensor

Oct 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992geoji.111..159r&link_type=abstract

Geophysical Journal International (ISSN 0956-540X), vol. 111, no. 1, p. 159-169.

Physics

8

Earth Gravitation, Gravitational Fields, Gravity Gradiometers, Spectrum Analysis, Tensors, Eigenvalues, Eigenvectors, Geodesy, Spherical Harmonics

Scientific paper

It is shown that, when the five independent components of the gravity tensor are grouped into (Gamma-zz), (Gamma-xz, Gamma-yz), and (Gamma-xx - Gamma-yy, 2Gamma-xy) sets and expanded into an infinite series of pure-spin spherical harmonic tensors, it is possible to derive simple eigenvalue connections between these three sets and the spherical harmonic expansion of the gravity potential. The three eigenvalues are (n + 1)(n + 2), -(n + 2) sq rt of n(n + 1), and sq rt of (n - 1)n(n + 1)(n + 2). The joint ESA and NASA Aristoteles mission is designed to measure with high precision the tensor components Gamma-zz, Gamma-yz, and Gamma-yy, which will make it possible to determine the global gravity field in six months time with a high precision.

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